Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 2x + 8$ and $ JT = 3x + 5$ Find $CT$.
A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {2x + 8} = {3x + 5}$ Solve for $x$ $ -x = -3$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 2({3}) + 8$ $ JT = 3({3}) + 5$ $ CJ = 6 + 8$ $ JT = 9 + 5$ $ CJ = 14$ $ JT = 14$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {14} + {14}$ $ CT = 28$